Investigation of Nonlinear Vibrations of A Cantilever Beam with A Transverse Fatigue Crack

Document Type : Research Article

Authors

1 Faculty of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, Iran.

2 Faculty of Aerospace Engineering, K. N. Toosi University of Technology, Iran

3 Faculty of Aerospace Engineering, K. N. Toosi University of Technology,Tehran, Iran.

Abstract

Nonlinear vibrations due to the presence of fatigue cracks are suitable indicators for detecting cracks in the structure. Late detection of such cracks may lead to catastrophic failures. Therefore, identifying the behavior of the cracked structure is very important for the prevention of structural failures. In this study, the nonlinear vibration of a cantilever beam with a transverse breathing crack and bilinear behavior has been studied. For this purpose, the restoring force of the cracked beam is considered a nonlinear polynomial function. Then, using the method of multiple scales, the approximated equation of the cracked beam is solved, and the frequency-response curves for both harmonic and superharmonic resonances are extracted. Then, the sensitivity of the responses to the crack depth, crack location, excitation force amplitude, and damping coefficient are investigated. The cracked beam frequency-response curves in the primary resonance have become highly nonlinear due to the increase of the crack parameters and cause softening of the curves. Also, it was observed that the behavior of the beam in superharmonic resonance is highly sensitive to the presence of a fatigue crack in the structure.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 10
January 2022
Pages 5069-5084

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